The moment conditions or estimating equations for instrumental variables quantile regression involves the discontinuous indicator function. We instead use smoothed estimating equations, with bandwidth h. This is known to allow higher-order expansions that justify bootstrap refinements for...

The literature has two types of fractional order statistics: an `ideal' (unobserved) type based on a beta distribution, and an observable type linearly interpolated between consecutive order statistics. We show convergence in distribution of the two types at an O(n-1) rate, which we also show...

We propose a nonparametric method to construct confidence intervals for quantile marginal effects (i.e., derivatives of the conditional quantile function). Under certain conditions, a quantile marginal effect equals a causal (structural) effect in a general nonseparable model, or equals an...

Estimation of a sample quantile's variance requires estimation of the probability density at the quantile. The common quantile spacing method involves smoothing parameter m. When m, n → ∞ , the corresponding Studentized test statistic asymptotically follows a standard normal...

In its favor, the common Kolmogorov–Smirnov test: 1) is distribution-free and non- parametric, 2) provides uniform confidence bands for the CDF by inversion, 3) may be interpreted as a family of pointwise tests controlling the familywise error rate, 4) can be calibrated to have exact...

Using and extending fractional order statistic theory, we characterize the O(n−1) coverage probability error of the previously proposed confidence intervals for population quantiles using L-statistics as endpoints in Hutson (1999). We derive an analytic expression for the n−1 term,...

We provide novel methods for inference on quantile treatment effects in both uncon- ditional and conditional (nonparametric) settings. These methods achieve high-order accuracy by using the probability integral transform and a Dirichlet (rather than Gaus- sian) reference distribution. We propose...